Update: Peazip and xz both worked!
The trick was to download the file again from the website every single time I tried to unzip it. But for example if I downloaded it and it failed with 7-zip, then unzipping the same file with peazip or xz didn't work even though 7-zip didn't seem to modify the file.
But once I downloaded the file again, then used peazip, it worked. Same: if I downloaded it again and then ran xz.
It was always the same file from the same site, and the download appeared to work fine every time, so I think somehow the failed try (regardless of program) was corrupting it.
Thanks again all. This was really bugging me and am gald be able to get started.